Can anybody give me a single word for a secluded garden surrounded by a wall?
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It's actually called "walled garden"
Curiously, the literal meaning of the word "paradise" IS "walled garden" but it has long since lost that meaning
Maybe you can also use hortus conclosus
What came to mind are the ancient Roman homes where the second half of the house is surrounded by a peristyle. The use of the word peristyle would be specific to a colonnade with a covered walkway and may not always contain a garden. However, I have seen peristyle garden and peristyle courtyard as alternatives. There is also a cloister, the medieval equivalent.
Secret garden is another possibility.
Perhaps you could try plantiecrub, although this source here suggests it would be for growing cabbage.